Comparative Analysis and Assessment of Economic Profitability of a Hybrid Renewable Energy Framework via HOMER Optimization in Jordan

Various developing and developed nations worldwide agreed on the considerable effectiveness of RE projects and alternative RE resources because of their expected successful results observed and practical relevance and benefits obtained from running solar PV, wind, bio, hydro, ocean, tidal, and other RE projects, reflected in (I) mitigating severe concentrations of Greenhouse Gas (GHG) emissions in the atmosphere, (II) providing sustainable energy resources as the fossil fuels will deplete, (III) minimizing other ecological issues noted globally, such as lower air quality, air pollution from particulate matter, global warming and climate change, and severe weather events associated with extremely hot days or very cold winters occurred in the recent years, and (IV) offering more cost-effective clean electrical power generation instead of fluctuating crude oil prices [1-5].

RE systems, either of small scales, like residential, commercial, and agricultural, large-scale for industrial purposes, or utility-size RE frameworks, which do include community RE plants, practical to supply necessary electricity for urbanized zones, do express essential chance for stable energy provision, helping make societies more resilient, sustainable, and more independent from different problems involved in fossil fuels. RE projects do also support in eliminating different negative impacts and severe issues correlated with fossil fuels, contributing to cleaner local environment [6, 7].

Generally, the available RE plants and systems that are commonly installed and prevalent in the RE market do contain one RE resource, like solar PV systems and wind farms. Nonetheless, relying solely on one RE resource of clean electricity may not achieve enhanced levels of ultimate energy production and amount of annual electricity yields per annum. For this reason, scholars and RE practitioners did shift into other frameworks of RE systems, which do consider utilizing one RE resource with a storage or a HRES that produces electricity from more than one RE resource and can utilize an energy storage technology [8-10].

The following paragraphs do express detailed analysis and in-depth discussions of various optimization and sensitivity analytical works conducted relying on mathematical modeling and numerical simulations by multiple advanced software packages to identify the profitability, feasibility, and practicality of RE systems, giving s special focus on HRESs, which do comprise more than one RE resource to offer sufficient electrical energy needs for local citizens.  

From the available literature, it can be realized that various scholars in the last decades have innovated new software tools that have flexible capabilities of identifying the optimum components that should exist in each HRES to offer the best economic feasibility (expressed in LCOE) and lower adverse environmental impacts in terms of carbon dioxide and other GHG emissions and enhanced air quality characterized by very low particulate matter in the air. For instance, BlueSol, PVsyst, Helioscope, Pylon, SolarEdge Site Designer, and PV-Sol software tools were developed to manage good estimation and efficient design of different small and large-size solar PV projects worldwide [11-16]. At the same time, WindSim, WindStation, Meteodyn WT, and Windie program packages were innovated to help design various on- and off-shore wind farms more appropriately and smoothly [17, 18].

A unique example of an advanced software tool that has been broadly utilized by researchers and RE experts to estimate the LCOE is the HOMER® software tool. The available literature comprises various articles discussing the beneficial impacts and crucial LCOE findings from HOMER® software adoption. However, there is a considerable lack of publications that address the employment of this valuable software for different Jordanian provinces [19-27].

Regarding international experience in this software tool, diverse scholars reported some contributory outcomes and vital economic profitability measures that help assess and compare the financial effectiveness and feasibility of HRESs. For instance, Abdin and Mérida [28] guided an analysis exploring the LCOE rates of multiple RE systems correlated to off-grid power systems using hydrogen energy as a storage bank. The authors analyzed nine different RE frameworks considering battery and hydrogen technologies. They took into account five locations worldwide, which were Brisbane, California, Colorado, Los Angeles, and Golden from the USA, besides Adelaide from South Australia, Squamish from Canada, and Australia. The scientists employed various RE configurations, focusing mainly on solar PV and wind to help generate clean electrical power. They also relied on hydrogen energy and batteries to provide a storage bank that can store excess electricity when it is not utilized. Based on the simulation processes and mathematical modeling of the nine investigated RE systems, it was found that the most cost-effective RE configurations could depend on specific geographic regions. Additionally, the results revealed that the minimal LCOE for a PV, wind turbine, battery bank, electrolyzer, and hydrogen storage tank integrated into Golden, Colorado, USA, was 0.50 USD/kWh. Furthermore, the bare minimum LCOE was determined when the battery bank was excluded, corresponding to 0.78 USD/kWh for the same site. The higher price level was primarily attributable to the cutting-edge hydrogen technologies that are integral parts of the system. Depending on these findings, it was discovered that hydrogen storage technology could offer longer-term energy storage technology solutions (ESTSs) for off-grid RE systems due to its significant cost-effectiveness compared with batteries. Also, it was found that using those RE models had offered helpful gains for the nature and ecological systems due to the exclusion of fossil fuels and GHG emissions generation that are directly responsible for global warming and climate change.

Bošnjaković et al. [29] conducted numerical simulations aiming to evaluate a series of profitability measures and economic metrics of HRESs to offer means of clean electrical power with very low electricity tariffs. The scholars clarified that the dramatic drop in PV prices helped avoid increasing rates of electricity prices and large environmental pressure and burden due to extensive reliance on fossil fuels. As a result, utility-scale PV projects have been broadly implemented on rooftops worldwide. The authors examined the financial viability of some PV systems under Croatian weather conditions to offer clean electrical power for families and homes in the rural continental part of the country. A house in Dragotin, Croatia, was selected as a case study. This dwelling had an annual electricity consumption of 4,211.70 kWh. Solar PV panels were installed with the best south-facing slop for this house. The HOMER® program was hired to determine the optimum size of the corresponding PV framework operating at 3.6 kW without the need of battery. The daily load curve was derived by monitoring the facility’s electricity consumption continuously throughout a typical June day. Daily load curves were created for a typical day in each month of the year because most of the activities involve power consumption and occur on a daily basis throughout most of the year. Hourly measures on the electricity generation of selected PV modules for a typical day in each month were obtained using the online platform Solargis Prospect, considering the insolation for the provided location. The amount of energy added to and drawn from the grid was determined using historical information. Based on the HOMER® software simulation work, the economic analysis confirmed that the PV system could offer a payback period for itself in 10.5 years without government subsidies when considering existing rates for selling and purchase of electricity, investment prices, and maintenance of equipment. Moreover, it was found that the overall investment for a 3.6 kW PV power plant amounted to 4,653 USD. From the network, 1,456.92 kWh of energy was consumed, while 2,754.14 kWh of energy was provided by the PV system. On the other hand, it was found that the PV system had the potential to export 1,804.32 kWh. The price of electricity with a Value-Added Tax (VAT) of 13% reached 0.150 USD/kWh, which is considered the highest electrical tariff. In comparison, the lower electricity tariff reached 0.083 USD/kWh. The average unit price of electrical power without excise duties was recorded at a rate of 0.069 USD/kWh. Furthermore, these green systems have a great potential for minimizing GHG emissions because fossil fuels are not employed.

To evaluate the viability of using renewable energy sources at two urban farm sites in Malaysia, the authors of Teo and Go [30] developed a solar PV/hybrid/storage system seeking to estimate its performance when the building geometry modeling process was considered with the help of optimal energy yield estimation techniques. The scholars reported that vertical farms consumed between 430.116 kWh and 1,002.024 kWh of electricity every day. Their proposed solar PV/hybrid/storage system for these vertical farming facilities was the focus of their investigation. The researchers evaluated the energy yield, Performance Ratio (PR), economics, and environmental impact. In two locations, grid-connected solar PV systems met between 11.6 and 8.35% of the load usage. According to the HOMER® mathematical simulations, it was found that grid-connected solar PV systems offered lower values of LCOE and attained considerable performance ratios corresponding to 82.22% and 82.56% at Selangor and Sarawak, respectively. Nonetheless, a freestanding hybrid PV-battery-diesel system contributed to the most remarkable LCOE and the lowest performance ratios (with 69.60% and 70.91%, subsequently). The researchers utilized a collection of mathematical correlations for more amended analysis of HRES in their work, including the necessary row spacing between PV modules, $D_{ {Row,PV }}$, which can be expressed by:

$D_{ {Row }, P V}=h_{ {Tilt }, P V}[\cos \gamma / \tan \varphi]$          (1)

where, $h_{ {Tilt }, P V}$ indicates the height of the tilted PV modules, $\gamma$ is the azimuth angle, and $\varphi$ expresses the solar attitude corresponding to certain solar time. γ can be calculated from the algebraic relationship:

$\sin \gamma=\left(\frac{\cos \delta \sin \omega}{\cos \varphi}\right)$         (2)

where, ω is the hour angle and δ is the angle between the sun and equatorial plane. Besides, they considered another expression related to the calculation of grid-tied PV power, which can be illustrated in the following:

$P_{{On.Grid.PV }}=D F_{P V} P_{ {Rated }, P V}\left(I_G / I_{S, P V}\right)$      (3)

where, $P_{ {on.Grid.PV }}$ is the derating factor of PV panels, $P_{ {Rated, } P V}$ is the rated power of single $\mathrm{PV}$ module, $I_G$ is the global solar incident irradiation on the surface of PV arrays, and $I_{S, P V}$ displays the standard solar irradiation considered in rating the overall PV array capacity. Also, the crucial formula considered to compute the PV cell temperature, $T_{ {Cell.PV }}$, was examined as follows:

$T_{ {Cell.PV }}=T_{A m b} \times\left(1+\frac{N O C T_{P V}-T}{I_{S, P V}} \times H_{A v g}\right)$        (4)

where, $T_{A m b}$ is the ambient temperature, $N O C T_{P V}$ is the nominal operating cell temperature, and $H_{A v g}$ is the average solar irradiation. To evaluate the total capacity of the HRES’s battery, they utilized the following correlation:

$B C_{ {Tot }}=T_{ {Amb }} \times\left(1+\frac{E L_{ {Daily }} \times A u t_{ {Days }}}{N V_{ {Batt }} \times \eta_{ {Batt }} \times D O D_{ {Batt }}} \times H_{{Avg }}\right)$        (5)

where, $E L_{ {Daily }}$ is the electrical daily load, $A u t_{ {Days }}$ is the number of autonomy days, $N V_{\text {Batt }}$ is the battery’s nominal voltage, $\eta_{ {Batt }}$ is the battery efficiency, and $DOD_{\text {Batt }}$ is the battery’s depth of discharge. On the other hand, modeling of the LCOE was conducted in their work. The corresponding LCOE formula can be expressed by:

$L C O E=\left(\frac{N P C}{\left(\sum_{t=0}^{8,760} \frac{P_{ {Load }}}{1,000}\right)\left(S L_{ {Tot }}\right)}\right)$      (6)

where, NPC is the net present cost, $P_{{Load }}$ is the load throughout, and $S L_{T o t}$ is the overall system lifespan. Figure 1 displays the normalized RE production in the two investigated sites in their work.

Referring to local HRESs conducted in different Jordanian provinces, the literature does consist of multiple publications, involving certain discussions and investigations of RE and HRES relevance for considerable sustainability and monetary feasibility. For example, researchers [31-46] did conduct analytical research, investigating possible advantages, critical contributions, and various feasible impacts of HRESs in supplying sufficient scales of electrical energy with better LCOE values, taking into consideration optimization, sensitivity analysis, and alleviation of adverse fossil fuel impacts on environment.

1.png

Figure 1. Normalized RE production from the HRESs investigated in the work of Teo and Go (2021), including grid-tied PV system (a) site #1 and (b) site #2

For instance, Al-Masri et al. [47] explored all probable on-grid RE frameworks necessary for covering the electrical load linked to Al-Mastaba district, Jordan. Relying on the minimization procedure of the case study’s objective function related to the Grid Usage Factor (GUF), the latter index was minimized utilizing optimizations by the flow direction optimization algorithm (FDOA). Corresponding grid-tied HRESs included (a) PV only, (b) wind only, (c) hybrid PV/ wind, (d) PV/ pumped-hydro energy storage (PHES), (e) wind/ PHS, and (f) hybrid PV/ wind/ PHS.

For every scene, optimum sizing and RE management strategies were accomplished utilizing FDOA. The critical indices comprised the number of PV modules, the number of wind turbines, and/ or the upper reservoir (UR) height correlated to the PHES facility (h_hydro). Crucial measured input hourly databases linked to major systems’ parts have been provided from formal organizations to help offer realistic and future actual-life outcomes and future directions. The optimization findings affirmed that HRES of [(PV/ wind/ PHES), which expresses scenario #6] had the optimum effectiveness.

It had the least GUF that reached an amount of 0.59%. It comprised 12,692 solar modules, 28 wind turbines, and a UR of 106.98 m pertaining to h_hydro. Additionally, the uncertainty analysis on measured input databases was adopted to check the system’s robustness. It was noted that the 6th scene of the HRES produced a rate of 122.29 t/year of carbon dioxide emissions.

The corresponding RE storage coefficient was 63.72%, offering an LCOE of 0.042 USD/kWh, expressing the least LCOE level. The authors confirmed that their method proposed in their work is remarkably suggested for any place to help minimize grid purchases, offering alternative solutions of electrical energy to local electricity networks.

In the same manner, Bataineh and Al-Mofleh [48] conducted a profitability analysis and performance investigation concerning an HRES that could cover the overall electrical loading of the Um-Jamal, Mafraq, Jordan.

The authors utilized the HOMER® software to conduct necessary optimizations and sensitivity analysis. The HRES contained a diesel generator, power converter, primary electrical load of overall Amman populations, wind turbine, and PV modules, as illustrated in Figure 2.

2.png

Figure 2. The overall HRES analyzed in the work of Bataineh and Al-Mofleh [48]

Referring to HOMER® optimization procedures, it was found that the first three scenarios included HRESs of ([a] PV, batteries, and power converter, [b] PV, batteries, power converter, and diesel generator, and [c] PV, wind, batteries, power converter, and diesel generator), corresponding to LCOE rates of 0.186, 0.183, and 0.199 USD/kWh, respectively.

Figure 3 indicates critical monetary variables related to the second HRES scenario.

3.png

Figure 3. Critical monetary variables related to the second HRES situation in the work of Bataineh and Al-Mofleh [48]

Within this framework of background, it can be realized from preliminaries that continuous research and development (R&D) performed on HRESs have contributed to the innovation of more profitable, workable, and practical HRESs that consider utilizing multiple breakthrough ESTSs. Those state-of-the-art evolutions in the HRESs and ESTSs brought considerable amendments and enhancements to various HRESs utilized universally in terms of efficiency, robustness, reliability, cost feasibility, and ecological sustainability. Technically speaking, remarkably amended Li-ion batteries and other sorts of ESTSs helped expand the overall autonomy days and storage duration through which ESTSs could serve small- and large-scale facilities. Referring to local experience, RE companies in Jordan did follow global path of RE investment, evolution, and improvement, which can be noted in domestic, commercial, and community-scale PV projects and wind farm that utilized latest RE technologies and took into application the most advanced RE designs, products, and frameworks.

Additionally, as can be observed from frequent prosperous RE outcomes in Jordan linked to (a) economic profitability, (b) green environmental impacts, and (c) lower adverse air quality effects and deleterious emissions, many Jordanian scholars and investors involved recent publications, peer-reviewed papers, and RE investment in the field of RE in upgrading universal and local RE industry through novel HRES models, new RE concepts, and more feasible ESTSs to help make RE prevalent and robust internationally and in Jordan.

Correspondingly, this work contains some sections that address and discuss a group of RE themes correlated to HRES investigation in Karak. These sections are arranged in the following sequence:

Section 2 indicates the Materials and Methods that will describe the relevant ideas regarding the major research phases and analytical process utilized in this paper.

Section 3 addresses the critical numerical Outcomes obtained from the mathematical simulations and sensitivity analysis adopted in the research method to calculate the LCOE linked to the HRES.

Section 4 represents the Conclusions that summarize the main findings represented and explained in the previous section to categorize and elucidate the vital contributions of RE and HRES for economic effectiveness and ecological benefits.

Section 5 describes the Future Work of this research recommended to foster and elaborate on the primary outputs of this article.

In this section, the main findings obtained from the numerical analysis conducted with the help of the HOMER® software are represented in detail.

The following paragraphs indicate the overall cases and scenarios found from the HRES considered and analyzed in this paper.

3.1 The overall scenarios of the investigated HRES

After defining the entire technical parameters and important financial variables for each component in the HRES, the HOMER® software found ten feasible cases/ scenarios. These outputs were attained based on a group of fiscal criteria and economic indices that best describe the cost-effectiveness, economic feasibility, and profitability of the ten hybrid RE configurations. Before introducing Table 9, the symbols (abbreviations) in this table should be clarified, as follows:

1) Net Present Cost (NPC),

2) Operating Cost (OC),

3) Capital Expenditure (CAEX).

These essential indices are mostly utilized and considered in different papers and works involving optimization of HRESs.

It can be inferred from the numerical findings represented in Table 9 that the most cost-effective HRES is the one that has the lowest value of LCOE, which is the first scenario that takes into account PV modules, wind turbine, diesel generator, Li-Ion battery, and power converter. The LCOE of this scenario amounts to 0.294 USD/kWh. Nonetheless, this scene may not be environmentally friendly because it relies on a diesel generator as a backup. As a result, carbon emissions are generated. On the other hand, the second case comprises all the components considered in this work, except PV modules. But excluding the PV system from this configuration does not provide more cost-effectiveness, which can be interpreted with larger LCOE due to the more considerable initial capital cost of the whole system. The exclusion of the PV system led to an LCOE of a 0.300 USD/kWh. Regarding the third case, only the wind turbine is excluded from the whole HRES. Consequently, when the wind turbine was not considered, the LCOE was higher. In turn, it contributed to a value of 0.393 USD/kWh. In case number 4, two components were excluded, which were PV system and Li-ion battery. Thus, it is predicted that excluding those critical components would lead to larger LCOE, which recorded an amount of 0.440 USD/kWh. Similarly, it is worth noting that excluding the Li-ion battery from the HRES would result in the same LCOE rate realized in the fourth case. However, in the last two cases, it can be observed that using no diesel generator would contribute to expensive LCOE. This aspect may be interpreted due to the shortage of energy storage capacity, by which clean electrical power might be lost without any utilization or storage for later use. At the same time, this research should remark that the higher values shown in Table 8 do not necessarily reflect poor economic feasibility due to the higher LCOE quantities. The reason goes back to the fact that this HRES is installed to serve clean electricity for 62,467 households in Karak (which corresponds to community/ utility load) but not for a single customer or a small home. For this reason, the LCOE of these community RE configurations would be considerable. Another clarifying graphical illustration of LCOE linked to the nine scenarios, expressed in Table 9 is displayed in Figure 13.

13.png

Figure 13. A summary of major LCOE rates and NPCs related to the nine investigated scenarios of this work

A clarifying column graph, distinguishing the influence of LCOE rate (cost feasibility) when diesel generator and/ or Li-ion battery do exist, can be expressed in Figure 14.

Table 9. The critical numerical outcomes of fiscal statistics and economic results for the ten hybrid RE scenarios/ cases

#	Scenario/ Case Architecture					Financial Details and Economic Measures				System
	9a.png	9b.png	9c.png	9d.png	9e.png	NPC (Billion USD)	LCOE (USD/kWh)	OC (Million USD/yr)	CAEX (Billion USD)	RE Fraction (%)
1	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	5.03	0.294	282	1.38	59.2
2		$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	5.13	0.300	295	1.32	57.7
3	$\checkmark$		$\checkmark$	$\checkmark$	$\checkmark$	6.71	0.393	378	1.81	34.6
4		$\checkmark$	$\checkmark$		$\checkmark$	7.52	0.440	497	1.09	30.1
5	$\checkmark$	$\checkmark$	$\checkmark$		$\checkmark$	7.52	0.440	495	1.12	30.8
6	$\checkmark$		$\checkmark$		$\checkmark$	10.6	0.621	714	1.39	0
7			$\checkmark$			11.4	0.665	855	0.305	0
8	$\checkmark$	$\checkmark$		$\checkmark$	$\checkmark$	14.2	0.831	345	9.73	100
9	$\checkmark$			$\checkmark$	$\checkmark$	26.4	1.54	495	20.0	100

14.png

Figure 14. Effect on involving diesel generator and/ or Li-ion battery energy storage on LCOE of this study [0 = not exist, 1 = exists]

It can be inferred from the data explained in Figure 14 that the existence of diesel generator does adversely impact the rate of LCOE, contributing to more increase (like in scenario No. 8 and 9), besides its negative impact on environment. On the contrary, if Li-ion battery is utilized, it could make the HRES more feasible by lowering the LCOE scale (like in scenario No. 4, 5, 6, and 7). However, it should be noted that Scenarios 1, 2, and 3 were more cost-effective than 4, 5, 6, and 7. The reason of this outcome is correlated to the existence of alternative feasible RE resources like PV alone, wind alone, or PV and wind. Resultantly, LOCE rate would be become lower, contributing to more profitability. 

The outcomes of this work are consistent with the findings of some researchers, who also utilized the HOMER® software in their work, like [39], stated that the LCOE of a community/ utility-scale load devoted to clean electrical power generation to a population of roughly 100,000 in Bangladesh amounted to 375 USD/MWh (or 0.375 USD/kWh). While scholars in [40] who developed a HRES for a community in Namibia found that the LCOE of this utility-scale HRES was (443 USD/MWh or 0.443/kWh) and (380 USD/MWh or 0.380 USD/kWh), corresponding to small and community loads of 1.7 kWh/day and 5.5 MWh/day, respectively. A third study in [41] revealed that after the HOMER® program to design a HRES for a rural community, it was found that the LCOE range of diesel (only) recorded LCOE rates between 920 USD/MWh (0.920/kWh) and 1,300 USD/MWh (or 1.30 USD/kWh), which is very expensive. Also, those authors mentioned that the solar PV system accomplished an LCOE of (400 USD/MWh (0.40 USD/kWh) to 610 MWh/USD (0.61 USD/kWh). Meantime, hybrid solar PV/diesel attained an LCOE of (540 USD/MWh [0.54 USD/kWh] to 770 USD/MWh [0.77 USD/kWh]), indicating that diesel is the most expensive technology.

In all cases, and from the review of literature, either authors [39-41], or other researchers, who carried out an LCOE analysis using the same software (HOMER®), confirmed that excluding diesel generators from the HRES is considerably preferable in terms of active prevention of GHG emissions and minimization of LCOE, helping fufill optimum profitability and enhanced cost-effectiveness.

Table 10. A comparison between hybrid RE projects and general RE systems in terms of different aspects

Table 11. A comparison between the LCOE obtained from this work with other scientists

3.2 Comparative analysis of HRES

To clarify the advantageous impacts of HRESs, it is worth conducting a clear comparison that best describes the critical benefits of HRESs compared with normal RE projects. Consequently, Table 10 is developed to explain the major technical gains and beneficial values of installing HRESs compared with regular RE framework.

3.3 Comparative analysis of the LCOE

On top of previous findings fulfilled from the HOMER optimization, it is important to compare the contributory outcomes of this work by validating the values of the LCOE attained in this numerical analysis with the LCOE from other scholars. In this context, another comparative analysis was conducted to express different LCOE amounts realized by various researchers. Table 11 represents this comparative investigation linked to the LCOE.

It can be noted from the comparative analysis conducted in Table 11 that the LCOE of this work was relatively acceptable and satisfying due to the existence of similar amounts that are closer to LCOE values of this work, like what other researchers found.

In addition, it is worth mentioning that some of the LCOE outcomes of this work (like scenarios one and two, (corresponding to LCOE of 0.294 and 0.300, respectively), were feasible when compared with the current electrical tariffs in Jordan, which is illustrated in row No. 6, including residential and commercial electrical tariffs.  

It is also important to explain that utilizing ESTSs in any HRES can increase its resilience, durability, reliability, and efficiency. As a result, its profitability and cost-effectiveness can be also realized. Fortunately, with continuous R&D, the potential, performance, practicality, and economic because of longer storage duration and larger number of autonomy days of these modern and state-of-the-art ESTSs. Certainly, Li-ion batteries utilized in smart phones express an amended form of ESTSs since of its extended resilience and durability. The latest styles and models of Li-ion batteries possess considerably enhanced storage capacity, DOD, lower charging duration, and extended lifespan, helping increase the resilience of overall HRESs.

Building on the numerical findings and statistical outcomes obtained from this work, this work proposes a set of critical possible fields of enhancements that could be followed to amend the robustness of the article’s outcomes. These essential future work directions include the following:

1) To conduct the same numerical analysis, taking into account additional RE components, like thermal energy, bioenergy, hydropower, or other RE resources;

2) To consider the implementation of other feasible ESTSs, like flywheels;

3) To utilize another optimization and simulation software or optimization algorithms and compare the accuracy and LCOE rates attained from those approaches;

4) To utilize correcting factors and specific electrical energy indices in the network to consider the power loss and variating load in certain days with peak demand.